IV: Non-Integrable Real Functions

In the context of the complex-analytic structure within the unit disk
centered at the origin of the complex plane, that was presented in a
previous paper, we show that a certain class of non-integrable real
functions can be represented within that same structure. In previous
papers it was shown that essentially all integrable real functions, as
well as all singular Schwartz distributions, can be represented within
that same complex-analytic structure. The large class of non-integrable
real functions which we analyze here can therefore be represented side
by side with those other real objects, thus allowing all these objects
to be treated in a unified way.

- Introduction

- Preliminary Considerations
- Singularities of Real Functions
- Piecewise Polynomial Real Functions
- Locally Integrable Real Functions
- Extended Fourier Theory

- General Statement of the Problem
- Representation of Non-Integrable Real Functions
- Representation in the Extended Fourier Theory
- Conclusions and Outlook
- Acknowledgments
- Bibliography